Polarizabilities of carbon nanotubes: Importance of the crystalline orbitals relaxation in presence of an electric field

Abstract : The static polarizabilities of a series of zigzag single walled carbon nanotubes [(m, 0) with m = 3n for m ¼ 7-25] were computed by the coupled perturbed Kohn-Sham (CPKS) coupled method recently implemented in the periodic CRYSTAL code. This method makes it possible to compute both the longitudinal and transverse polarizabilities with the same approach including the local field depolarization effects for the whole series of the investigated nanotubes. To quantify these effects, the unscreened longitudinal and transverse polarizabilities were also calculated within the linear response theory using the Sum Over States (SOS) method. Our results confirmed the inverse-square dependence on the bandgap of the longitudinal polarizabilities which are found weakly affected by the crystalline orbital relaxation. On the other hand, the comparison between the screened (CPKS) and unscreened (Sum Over States) transverse polarizabilities permit to calibrate more precisely the classical correction of Benedict et al.